Feynman slash notation contracts a four-vector with the gamma matrices. With mostly-minus signature, the Clifford algebra gives , so away from the mass shell.
The Clifford algebra gives . Splitting a scalar-coefficient polynomial into even and odd powers proves the displayed reduction. For an on-shell fermion spin sum assumed to be such a polynomial, implies ; the normalization fixes in four spacetime dimensions.
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Feynman slash notation is a shorthand used primarily in quantum field theory to simplify the expressions involving Dirac spinors and gamma matrices. It is named after physicist Richard Feynman, who contributed significantly to the development of quantum electrodynamics and other areas of physics. In this notation, the slash is used to denote a contraction between a four-vector and the gamma matrices that appear in the Dirac equation.
